The Cuban government must give greater freedom to its people and “something in return” to the US if it wants to keep the new era of warmer relations with Washington alive, top aides to Donald Trump warned on Sunday, as the death of Fidel Castro three weeks after the US election thrust Cuba into uncharted territory.

Reince Priebus, Trump’s incoming chief of staff, said the president-elect would “absolutely” reverse Barack Obama’s stance on Cuba unless there was “some movement” from Havana.

“Repression, open markets, freedom of religion, political prisoners: these things need to change in order to have open and free relationships, and that’s what President-elect Trump believes, and that’s where he’s going to head,” Priebus said.

Kellyanne Conway, another top adviser to Trump, who denounced Fidel as a “brutal dictator” on Saturday, said any future deal would have to be in the interest of Americans.

“To the extent that President Trump can open up new conversations with Cuba, it would have to be a very different Cuba,” she told ABC television.

Barack Obama, Michelle Obama and their daughters with Cuban president Raúl Castro at a baseball game in Havana. Photograph: Jonathan Ernst/Reuters

“He wants to make sure that when the United States of America, when he’s president, engages in any type of diplomatic relations or trade agreements … that we as America are being protected and we as America are getting something in return.”

However, many restrictions remain in place and can only be removed by Congress. During the fight for presidential votes in Florida, home to many Cuban exiles, Trump and his running mate, Mike Pence, promised to reverse the executive orders that relaxed the half-century US embargo on the island.

Trump unlikely to reinstate embargo after death of Fidel Castro, analysts say

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But, although both men marked Fidel Castro’s death by denouncing his human rights record, they did not repeat the call to reinstate sanctions. Foreign policy analysts said that despite the trenchant tone of some of the comments from the Trump camp, the opening to Cuba was unlikely to be thrown away any time soon.

“He’s sending very strong signals that he’s going to take a hard line on Cuba but without giving specifics,” said Gregory Weeks, an expert on US-Cuban relations at the University of North Carolina in Charlotte.

The restoration of relations with the US and an easing of travel restrictions are two key ways in which Raúl Castro has made his mark on Cuban history since formally assuming power in 2008. He has cemented his personal power, maintained the hegemony of the Communist party and laid to rest the once widely held belief that Cuba would implode with the death of his brother.

But Fidel’s death and Trump’s impending presidency will test Raúl’s nerve and judgment as never before.

“Raúl is a transitional president between the old guard and the future … in that sense he has performed well. He has kept the country stable,” said Volker Skierka, a Fidel biographer and Cuba expert.

US policymakers have been forced to abandon their cherished theory that the Communist party’s grip on power would slip without Fidel. “As much as we wish otherwise, I don’t see it happening,” said a US diplomat in the region.

European diplomats went further, with one saying: “We won’t see a huge shift of Cuban politics … more significant would be if Raúl dies, because he put his leadership on the line for reform.”

Dissidents pose little threat to the government. They resonate internationally as symbols of opposition but foreign diplomats in Havana write them off as politically irrelevant on the island.

Raúl has released most political prisoners and allowed leading critics such as Rosa María Payá and Yoani Sánchez to travel abroad. But organised opposition at home is often met with arrests and beatings.

Raúl’s main test is raising living standards for the island’s 11.2 million people. The average monthly wage is less than £15, obliging people to scrabble for decent food and basics such as soap, and there are severe shortages of housing and transport.

“The economy is what’s most on people’s minds,” said Susan Kaufman Purcell, the director of the centre for hemispheric policy at the University of Miami.

Raúl, who studied Vietnam and China as models of communist parties which have retained control while freeing their economies, has trimmed the vast state bureaucracy and laid off hundreds of thousands of workers.

He has licensed hundreds of different types of micro-businesses, and told Cubans to stop blaming the embargo for their ills and to be “fearless” in criticising corruption, bureaucracy and inefficiency.

The reforms have allowed small new businesses to bloom, notably restaurants, guesthouses and stalls which have livened up Havana’s sleepy streets, but efforts to boost agriculture have fallen flat. Shortages of basic foodstuffs remain the norm.

The challenge is to deliver material improvements while retaining the free universal access to education and healthcare that is the revolution’s proudest boast and main pillar of legitimacy.

In contrast to Fidel’s marathon speeches and nocturnal habits, Raúl is a family man who speaks briefly and likes to be home for dinner. He delegates decisions to a small, trusted cabal. Raúl’s power base is the military, an institution he forged during 47 years as defence minister.

For the past decade, Venezuelan oil subsidies have been crucial to Cuba’s economy. President Nicolás Maduro is close to Raúl but Venezuela’s economy is collapsing. Should Maduro fall, alarm bells will sound across Havana.

Cuba learned the hard way not to become too dependent on a single sponsor. In the 1990s, after the collapse of the Soviet Union, the island’s economy was in tatters. Ever the pragmatist, Raúl has spent his years as president hedging against this possibility by nurturing ties with China, Russia, Latin America, the European Union and even the US.

But nobody should mistake that for a shift of ideology. In his 2016 speech to the party congress, Raúl echoed his brother’s calls for unity in the face of capitalist US influence. “If one day they manage to fragment us, that would be the beginning of the end of the revolution, of socialism and independence in our homeland,” he said.

Raúl’s other outstanding task is grooming a successor. He has repeatedly insisted a generational change is long overdue, but for the moment his inner circle is dominated by octogenarians. One reason is that younger colleagues lack the cachet of involvement in the 1959 revolution which overthrew the Batista dictatorship.

Nonetheless, Raúl has said he will stand down as president in 2018 and his first vice-president, Miguel Díaz-Canel, is widely tipped to assume his mantle.

Fidel’s death – expected to prove more of an emotional than political earthquake for Cuba – is unlikely to change that, but it could make change easier for the next generation of Cuban leaders.